Mathematics – Rings and Algebras
Scientific paper
2003-01-16
Mathematics
Rings and Algebras
Scientific paper
Suppose that $S$ is an incomplete inner product space. A. Dvure\v{c}enskij shows that there are no finitely additive states on orthogonally closed subspaces, $F(S)$, of $S$ that are regular with respect to finitely dimensional spaces. In this note we show that the most important special case of the former result--the case of the evaluations given by vectors in the ``Gleason manner''--allows for a relatively simple proof. This result further reinforces the conjecture that there are no finitely additive states on $F(S)$ at all.
Chetcuti E.
Pták Pavel
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